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Hilbert’s Conception of “Existence-in-Mathematics” and Modelling it by a Formal Axiomatic Theory Ф+⁆, Treating Existence not as the Quanifier but as a Modality

Authors

  • Vladimir Lobovikov Institute of Philosophy and Law UB RAS (Yekaterinburg)

DOI:

https://doi.org/10.47850/RL.2024.5.1.16-50

Abstract

The subject-matter of investigation is Hilbert’s-principle consisting of two parts: (a) proclaiming equivalence-of-consistency-and-truth-in-mathematics; (b) proclaiming equivalence-of-consistency-and-existence-in‑mathematics. The target – explication and vindication of the principle. The scientific novelty: for reaching the goal,
(1) a hitherto unknown logically formalized multimodal axiomatic epistemology-and-ontology-system called Ф+⁆ has been constructed; (2) by means of Ф+⁆ , a precise axiomatic definition of the notion “existence as modality” is submitted for the first time; (3) by means of artificial language of Ф+⁆ , a precise formulation of the principle-of-equivalence-of-consistency-and-existence is given; (4) for the first time, the article presents formal deductive inferences (in formal-theory-Ф+⁆ ) of such formulae which make up Hilbert’s principle (given an appropriate interpretation of these formulae).

Author Biography

Vladimir Lobovikov, Institute of Philosophy and Law UB RAS (Yekaterinburg)

Doctor of Philosophical Sciences, Professor, Principal Researcher

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2024-03-25

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Lobovikov В. О. (2024). Hilbert’s Conception of “Existence-in-Mathematics” and Modelling it by a Formal Axiomatic Theory Ф+⁆, Treating Existence not as the Quanifier but as a Modality . Respublica Literaria, 5(1), 16–50. https://doi.org/10.47850/RL.2024.5.1.16-50